Testing linearity of spatial interaction functions \`a la Ramsey

TL;DR

This paper introduces a simple, robust nonparametric test for assessing the linearity of spatial interaction functions, which are important in modeling spatial behaviors and interactions.

Contribution

It develops a computationally straightforward, heteroskedasticity-robust test based on the Lagrange Multiplier principle, applicable to spatial interaction functions.

Findings

The test controls size well in simulations.

It demonstrates high power in detecting nonlinearity.

Applied to Finnish data, it informs debates on tax competition.

Abstract

We propose a computationally straightforward test for the linearity of a spatial interaction function. Such functions arise commonly, either as practitioner imposed specifications or due to optimizing behaviour by agents. Our conditional heteroskedasticity robust test is nonparametric, but based on the Lagrange Multiplier principle and reminiscent of the Ramsey RESET approach. This entails estimation only under the null hypothesis, which yields an easy to estimate linear spatial autoregressive model. Monte Carlo simulations show excellent size control and power. An empirical study with Finnish data illustrates the test's practical usefulness, shedding light on debates on the presence of tax competition among neighbouring municipalities.